Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

L-Curve and Curvature Bounds for Tikhonov Regularization

The L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems by Tikhonov regularization. However, the computational effort required to determine the L-curve and its curvature can be prohibitive for large-scale problems. Recently, inexpensively computable approximations of the L-curve and its curvature, referred to as the L-ribbon and the curvature-ribbon, respectively, were proposed for the case when the regularization operator is the identity matrix. This note discusses the computation and performance of the L- and curvature-ribbons when the regularization operator is an invertible matrix.     

Half-width temperature dependence of nitrogen broadened lines in the ν2 band of H2O

Forty-seven N₂ broadened water vapor line-widths have been measured in the 1845-2140 cm⁻¹ spectral range with a Fourier Transform spectrometer in the 258-330 K temperature range at a spectral resolution of 0.005 cm⁻¹ for the lines with upper state rotational quantum number up to 16. The measured exponents of the temperature dependence of the width exhibit a large range of values from 1.60 to −0.86. Theoretical calculations were made using a semi-empirical technique based on the Anderson theory. The calculated broadening coefficients as well as the temperature exponents for the half-width agree satisfactory with measured values.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

Plasmon resonance in a nanosphere

The phenomenon of plasmon resonance in a nanosphere and a nanospheroid is considered. As is known, this phenomenon does not depend explicitly on the size of these nanoparticles. However, it is shown that, actually, the resonance conditions are determined by the diameter of the nanosphere and by the length of the major axis of the nanospheroid.     

Dependence of Doubly Charged Ion Formation by the Two-Electron Mechanism on the intensity of Laser Radiation

Experimental dependences of the doubly charged ion yield N ²⁺ on the laser radiation intensity F are analyzed for the case of ion formation by the two-electron mechanism. It is shown that the region where the dependence N ²⁺(F) is characterized by the degree of nonlinearity K≈2.5 corresponds to the saturation of the process of doubly charged ion formation. This region is described well by theoretical calculations performed for Gaussian laser beams.     

Mathematical modeling of the Magnus effect in the geometrical optics approximation

The Magnus effect in multimode fibers with triangular and parabolic refractive index profiles (RIPs) is simulated in the geometrical optics approximation. The calculations confirm the linear relation between the angle of rotation Δ? and the fiber length z. The results of calculations for a spiral path with constant radius are compared with the analytical solution obtained. For a fiber with a parabolic RIP, the value of Δ? obtained in this work is one-half the result obtained in the wave approach.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.